Abstract
In this paper we investigate on solid transportation problem with interval environment. In this manuscript we develop STP under interval unit transportation cost, availability, requirement, conveyances capacity etc. Also, separately from source, demand and capacity constraints, an additional constraint on the total budget at each destination is imposed. We employ two different approaches (Hu and Wang's Approach and Mahato and Bhunia's Approach) based on interval ranking. After converting the interval transportation models into its crisp equivalent we apply the Weighted Tchebycheff method to solve. The models are illustrated with numerical examples and solved using the LINGO.13 optimization software.
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References
Baidya A, Bera UK, Maiti M (2013a) Multi-item interval valued solid transportation problem with safety measure under fuzzy-stochastic environment. J Transp Secur 6:151–174
Baidya A, Bera UK, Maiti M (2013) Solution of multi-item interval valued solid transportation problem with safety measure using different methods, OPSEARCH, Springer, DOI 10.1007/s12597013 0129-2
Hu BQ, Wang S (2006) A novel approach in uncertain programming part i: New arithmetic and order relation for interval numbers. Journal of Industrial and Management Optimization 2(4):351–371
Shell E (1955) Distribution of a product by several properties, Directorate of Management Analysis in: Proceedings of the 2nd Symposium in Liner Programming, DCS/Comptroller H.Q.U.S.A.F., Washington, D.C., vol. 2, pp. 615–642.
Hitchcock FL (1941) The distribution of a product from several sources to numerous localities. Journal of Mathematical Physic 20:224–230
Ishibuchi H, Tanaka H (1990) Multi-objective programming in optimization of the interval objective functions. Eur J Oper Res 48:219–225
Jaulin L, Kieffer M, Didrit O, Walter E (2001) Applied Interval Analysis with Examples in Parameter and State Estimation. Robust Control and Robotics, Springer-Verlag, London
Kearfott RB (1996) Rigorous Global Search: Continuous Problems. Kluwer, Dor-drecht
Moore RE (1979) Methods and Applications of Interval Analysis. SIAM, Philadelphia
Moore RE, Kearfott RB, Cloud MJ (2009) Introduction to Interval Analysis. SIAM, Philadelphia
Chanas S, Kuchta D (1996) Multi-objective programming in optimization of interval objective functions – A generalized approach. Eur J Oper Res 94(3):594–598
Mahato SK, Bhunia AK (2006) Interval-arithmetic-oriented interval computing technique for global optimization. Applied Mathematics Research Express 2006:1–19
Kulpa Z (1997) Diagrammatic representation for a space of intervals. Machine Graphics and Vision 6(1):5–24
Kulpa Z (2001) Diagrammatic representation for interval arithmetic. Linear Algebra Appl 324:55–80
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Baidya, A., Bera, U.K. An interval valued solid transportation problem with budget constraint in different interval approaches. J Transp Secur 7, 147–155 (2014). https://doi.org/10.1007/s12198-014-0135-5
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DOI: https://doi.org/10.1007/s12198-014-0135-5